Related papers: Functional inequalities for generalized inverse tr…
The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2019}, is to propose several generalized inequalities for the ratio functions of trigonometric and hyperbolic functions. We basically follow the…
The generalized trigonometric functions occur as an eigenfunction of the Dirichlet problem for the one-dimensional $p-$Laplacian. The generalized hyperbolic functions are defined similarly. Some classical inequalities for trigonometric and…
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding…
In this paper, the versions of trigonometric functions of certain known inequalities for hyperbolic ones are proved, and then corresponding inequalities for means are presented.
In this paper we prove the conjecture posed by Kl\'en et al. in \cite{kvz}, and give optimal inequalities for generalized trigonometric and hyperbolic functions.
Bernoulli type inequalities for functions of logarithmic type are given. These functions include, in particular, Gaussian hypergeometric functions in the zero-balanced case $F(a,b;a+b;x)\,.$
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic sine.
In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
In this paper, new sharp bounds for circular functions are proved. We provide some improvements of previous results by using infinite products, power series expansions and a generalisation of the so-called Bernoulli inequality. New proofs,…
This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
In the article, some Huygens and Wilker type inequalities involving trigonometric and hyperbolic functions are refined and sharpened.
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.